Iterated upwind schemes for gas dynamics

A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave-propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness

Space-time residual distribution on moving meshes

International audienceThis article investigates the potential for an r-adaptation algorithm to improve the efficiency of space-time residual distribution schemes in the approximation of time-dependent hyperbolic conservation laws, e.g. scalar advection, shallow water flows, on unstructured, triangular meshes. In this adaptive framework the connectivity of the mesh, and hence the number of degrees of freedom, remain fixed, but the mesh nodes are continually "relo-cated" as the flow evolves so that features of interest remain resolved as they move within the domain. Adaptive strategies of this type are well suited to the space-time residual distribution framework because, when the discrete representation is allowed to be discontinuous in time, these algorithms can be designed to be positive (and hence stable) for any choice of time-step, even on the distorted space-time prisms which arise from moving the nodes of an unstructured triangular mesh. Consequently, a local increase in mesh resolution does not impose a more restrictive stability constraint on the time-step, which can instead be chosen according to accuracy requirements. The order of accuracy of the fixed-mesh scheme is retained on the moving mesh in the majority of applications tested. Space-time schemes of this type are analogous to conservative ALE formulations and automatically satisfy a discrete geometric conservation law, so moving the mesh does not artificially change the flow volume for pure conservation laws. For shallow water flows over variable bed topography, the so-called C-property (retention of hydrostatic balance between flux and source terms, required to maintain the steady state of still, flat, water) can also be satisfied by considering the mass balance equation in terms of free surface level instead of water depth, even when the mesh is moved. The r-adaptation is applied within each time-step by interleaving the iterations of the nonlinear solver with updates to mesh node positions. The node movement is driven by a monitor function based on weighted approximations of the scaled gradient and Laplacian of the local solution and regularised by a smoothing iteration. Numerical results are shown in two dimensions for both scalar advection and for shallow water flow over a variable bed * *Manuscript Click here to view linked References which show that, even for this simple implementation of the mesh movement, reductions in cpu times of up to 60% can be attained without increasing the error

Aeronautical engineering: A continuing bibliography with indexes (supplement 295)

This bibliography lists 581 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System in Sep. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Aeronautical engineering: A continuing bibliography with indexes (supplement 242)

This bibliography lists 466 reports, articles, and other documents introduced into the NASA scientific and technical information system in July, 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Space–time residual distribution on moving meshes

This article investigates the potential for an r-adaptation algorithm to improve the efficiency of space–time residual distribution schemes in the approximation of time-dependent hyperbolic conservation laws, e.g. scalar advection, shallow water flows, on unstructured, triangular meshes. In this adaptive framework the connectivity of the mesh, and hence the number of degrees of freedom, remain fixed, but the mesh nodes are continually “relocated” as the flow evolves so that features of interest remain resolved as they move within the domain. Adaptive strategies of this type are well suited to the space–time residual distribution framework because, when the discrete representation is allowed to be discontinuous in time, these algorithms can be designed to be positive (and hence stable) for any choice of time-step, even on the distorted space–time prisms which arise from moving the nodes of an unstructured triangular mesh. Consequently, a local increase in mesh resolution does not impose a more restrictive stability constraint on the time-step, which can instead be chosen according to accuracy requirements. The order of accuracy of the fixed-mesh scheme is retained on the moving mesh in the majority of applications tested. Space–time schemes of this type are analogous to conservative ALE formulations and automatically satisfy a discrete geometric conservation law, so moving the mesh does not artificially change the flow volume for pure conservation laws. For shallow water flows over variable bed topography, the so-called C-property (retention of hydrostatic balance between flux and source terms, required to maintain the steady state of still, flat, water) can also be satisfied by considering the mass balance equation in terms of free surface level instead of water depth, even when the mesh is moved. The r-adaptation is applied within each time-step by interleaving the iterations of the nonlinear solver with updates to mesh node positions. The node movement is driven by a monitor function based on weighted approximations of the scaled gradient and Laplacian of the local solution and regularised by a smoothing iteration. Numerical results are shown in two dimensions for both scalar advection and for shallow water flow over a variable bed which show that, even for this simple implementation of the mesh movement, reductions in cpu times of up to 60% can be attained without increasing the error

Aeronautical engineering: A continuing bibliography with indexes (supplement 253)

This bibliography lists 637 reports, articles, and other documents introduced into the NASA scientific and technical information system in May, 1990. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

The Dependence of the Time-Asymptotic Structure of 3-D Vortex Breakdown on Boundary and Initial Conditions

The three-dimensional, compressible Navier-Stokes equations are solved numerically to simulate vortex breakdown in tubes. Time integration is performed with an implicit Beam-Warming algorithm, which uses fourth-order compact operators to discretize spatial derivatives. Initial conditions are obtained by solving the steady, compressible, and axisymmetric form of the Navier-Stokes equations using Newton\u27s method. Stability of the axisymmetric initial conditions is assessed through 3-D time integration. Unique axisymmetric solutions at a Reynolds number of 250 lose stability to 3-D disturbances at a critical value of vortex strength, resulting in 3-D and time-periodic flow. Axisymmetric solutions at a Reynolds number of 1000 contain regions of nonuniqueness. Within this region, 3-D time integration reveals only unique solutions, with nonunique, axisymmetric initial conditions converging to a unique solution that is steady and axisymmetric. Past the primary limit point, which approximately identifies critical flow, the solutions bifurcate into 3-D periodic flows

A locally analytic density functional theory describing adsorption and condensation in microporous materials

The fluid density distribution within microscopic pores is determined by solving integral equations relating to the local chemical potential to the Van der Waals attractions and hard sphere repulsions of surrounding material. To avoid resolving the density distribution on sub-molecular scales, the governing equations are averaged over zones of molecular size using analytic functions to represent local density variations within each zone. These local density profiles range form singularities to uniform distributions depending on the local variation of the potential field. Sample calculations indicate that this integral approach yields results in very good agreement with those based on traditional density functional theory (DFT), while reducing computing times by factors of 10{sup 3} to 10{sup 4} for one- dimensional geometries

Computational Methods For The Diagnosis of Rheumatoid Arthritis With Diffuse Optical Tomography

Diffuse optical tomography (DOT) is an imaging technique where near infrared (NIR) photons are used to probe biological tissue. DOT allows for the recovery of three-dimensional maps of tissue optical properties, such as tissue absorption and scattering coefficients. The application of DOT as a tool to aid in the diagnosis of rheumatoid arthritis (RA) is explored in this work. Algorithms for improving the image reconstruction process and for enhancing the clinical value of DOT images are presented in detail. The clinical data considered in this work consists of 99 fingers from subjects with RA and 120 fingers from healthy subjects. DOT scans of the proximal interphalangeal (PIP) joint of each finger is performed with modulation frequencies of 0, 300, and 600 MHz. A computer-aided diagnosis (CAD) framework for extracting heuristic features from DOT images and a method for using these same features to classify each joint as affected or not affected by RA is presented. The framework is applied to the clinical data and results are discussed in detail. Then, an algorithm for recovering the optical properties of biological media using the simplified spherical harmonics (SPN) light propagation model is presented. The computational performance of the algorithm is analyzed and reported. Finally, the SPN reconstruction algorithm is applied to clinical data of subjects with RA and the resulting images are analyzed with the CAD framework. As the first part of the CAD framework, heuristic image features are extracted from the absorption and the scattering coefficient images using multiple compression and dimensionality reduction techniques. Overall, 594 features are extracted from the images of each joint. Then, machine-learning techniques are used to evaluate the ability to discriminate between images of joints with RA and images of healthy joints. An evolution-strategy optimization algorithm is developed to evaluate the classification strength of each feature and to find the multidimensional feature combination that results in optimal classification accuracy. Classification is performed with k-nearest neighbors (KNN), linear (LDA) and quadratic discriminate analysis (QDA), self-organizing maps (SOM), or support vector machines (SVM). Classification accuracy is evaluated based on diagnostic sensitivity and specificity values. Strong evidence is presented that suggest there are clear differences between the tissue optical parameters of joints with RA and joints without RA. It is first shown that data obtained at 600 MHz leads to better classification results than data obtained at 300 and 0 MHz. Analysis of each extracted feature shows that DOT images of subjects with RA are statistically different (p < 0.05) from images of subjects without RA for over 90% of the features. Evidence shows that subjects with RA that do not have detectable signs of erosion, effusion, or synovitis (i.e. asymptomatic subjects) in MRI and US images have optical profiles similar to subjects who do have signs of erosion, effusion, or synovitis; furthermore, both of these cohorts differ from healthy controls subjects. This shows that it may be possible to accurately identify asymptomatic subjects with DOT scans. In contrast, these subjects remain difficult to identify from MRI and US images. The implications of these results are profound, as they suggest it may be possible to identify RA with DOT at an earlier stage compared to standard imaging techniques. Results from the feature-selection algorithm show that the SVM algorithm (with a third order polynomial kernel) achieves 100.0% sensitivity and 97.8% specificity. Lower bounds for these results (at 95.0% confidence level) are 96.4% and 93.8%, respectively. Image features most predictive of RA are from the spatial variation of optical properties and the absolute range in feature values. The optimal classifiers are low dimensional combinations (< 7 features). Robust cross- validation is performed to ensure the generalization of these classification results. The SPN -based reconstruction algorithm uses a reduced-Hessian sequential quadratic programming (rSQP) PDE-constrained optimization approach to maximize computational efficiency. The complex-valued forward model, or frequency domain SPN equations (N = 1, 3), is discretized using the finite-volume method and solved on unstructured computational grids using the restarted GMRES algorithm. The image reconstruction algorithm is presented in detail and its performance benchmarked against the ERT algorithm. The algorithm is subsequently used to recover the absorption and scattering coefficient images of joints scanned in the RA clinical study. While the SPN model is inherently less accurate than the ERT model, it is nevertheless shown that the images obtained with the SP3-based reconstruction algorithm are sufficiently accurate and allow for the diagnosis of RA at clinically relevant sensitivity [87.9% (78.1%, 100.0%)] and specificity [92.9% (84.6%, 100.0%)] values (the 95.0% confidence interval is specified in brackets). In contrast to results obtained with the SP3 model, the images generated with the SP1 algorithm yield significantly lower sensitivity [66.7% (46.6%, 100.0%)] and specificity [81.0% (64.8%, 100.0%)] values. While some numerical accuracy is sacrificed by selecting the SP3 model over the ERT model, the superior computational performance of the SP3 algorithm allows for computation of the absorption and the scattering coefficient images in under 15 minutes and requires less than 200 MB of RAM per finger (compared to the over 180 minutes and over 6 GB of RAM needed by the ERT-based algorithm). Overall, results indicate that the SP3-based reconstruction algorithm provides computational advantages over the ERT-based algorithm without sacrificing significant classification accuracy. In contrast, the SP1 model provides computational advantages compared to the ERT at the expense of classification accuracy. This indicates that the frequency-domain SP3 model is an ideal light propagation model for use in DOT scanning of finger joints with RA. Altogether, the results presented in this dissertation underscore the high potential for DOT to become a clinically useful diagnostic tool. The algorithms and framework developed as part of this dissertation can be directly used on future data to help further validate the hypotheses presented in this work and to further establish DOT imaging as a valuable diagnostic tool

Transonic Symposium: Theory, Application, and Experiment, Volume 1, Part 1

Topics addressed include: wind tunnel and flight experiments; computational fluid dynamics (CFD) applications, industry overviews; and inviscid methods and grid generations